Write in Standard Form 10a(-6a^2+2a-7)

$10 a (- 6 a^{2} + 2 a - 7)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Apply the distributive property.

$10 a (- 6 a^{2}) + 10 a (2 a) + 10 a \cdot - 7$

Step 3

Simplify.

Rewrite using the commutative property of multiplication.

$10 \cdot - 6 a \cdot a^{2} + 10 a (2 a) + 10 a \cdot - 7$

Rewrite using the commutative property of multiplication.

$10 \cdot - 6 a \cdot a^{2} + 10 \cdot 2 a \cdot a + 10 a \cdot - 7$

Multiply $- 7$ by $10$ .

$10 \cdot - 6 a \cdot a^{2} + 10 \cdot 2 a \cdot a - 70 a$

Step 4

Simplify each term.

Multiply $a$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$10 \cdot - 6 (a^{2} a) + 10 \cdot 2 a \cdot a - 70 a$

Multiply $a^{2}$ by $a$ .

Raise $a$ to the power of $1$ .

$10 \cdot - 6 (a^{2} a^{1}) + 10 \cdot 2 a \cdot a - 70 a$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 \cdot - 6 a^{2 + 1} + 10 \cdot 2 a \cdot a - 70 a$

Add $2$ and $1$ .

$10 \cdot - 6 a^{3} + 10 \cdot 2 a \cdot a - 70 a$

Multiply $10$ by $- 6$ .

$- 60 a^{3} + 10 \cdot 2 a \cdot a - 70 a$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$- 60 a^{3} + 10 \cdot 2 (a \cdot a) - 70 a$

Multiply $a$ by $a$ .

$- 60 a^{3} + 10 \cdot 2 a^{2} - 70 a$

Multiply $10$ by $2$ .

$- 60 a^{3} + 20 a^{2} - 70 a$